-1
$\begingroup$

I have to show that if $f:[a,+\infty [\longrightarrow \mathbb R$ is uniformly continuous, then $\lim_{x\to +\infty }f(x)=+\infty $. I spend very much time on it, and I can't conclude. How can I find a $\delta>0$ s.t. $|f(x)-f(y)|<\varepsilon$ if $|x-y|<\delta$ for all $\varepsilon>0$ ?

$\endgroup$

closed as unclear what you're asking by GEdgar, Silvia Ghinassi, miracle173, Daniel Fischer Feb 5 '16 at 18:24

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    $\begingroup$ A constant function $f:x \mapsto c$ is uniformly continuous but $\lim\limits_{x\to +\infty }f(x)=c$ is finite. $\endgroup$ – Watson Feb 5 '16 at 16:26
  • $\begingroup$ it seems the question is wrong. $\endgroup$ – runaround Feb 5 '16 at 16:29
  • $\begingroup$ Therefore, should be closed as "unclear what you are asking". $\endgroup$ – GEdgar Feb 5 '16 at 16:29
4
$\begingroup$

A constant function $f:x \mapsto c$ is uniformly continuous but $\lim\limits_{x\to +\infty }f(x)=c$ is finite.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.